Finding speed of roller coaster at different points

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To find the speed of a roller coaster at different points, the discussion emphasizes the conversion of potential energy (PE) to kinetic energy (KE). At the highest point (P1), the roller coaster has only potential energy, while at a lower point (P2), this energy converts entirely into kinetic energy. The equation PE1 = KE2 is used to establish the relationship between the heights and speeds, leading to the calculation of speed at P2 as 26.19 m/s. There is confusion regarding the relationship between kinetic energy at P2 and potential energy at P3, suggesting that a similar method can be applied to find the speed at P3 using the height difference. Understanding energy conservation principles is crucial for solving the problem effectively.
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Homework Statement



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Homework Equations



KE= 1/2 m v2
PE = mgy

The Attempt at a Solution



I'm not sure how to start this because there is no given mass. If I use a kinematics equation I don't have an acceleration.
 
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At point 1, the roller coaster only has potential energy (no kinetic energy because velocity is 0). At point 2, it will have lost all of its potential energy - the potential energy will have been converted into kinetic energy. Since no energy is being lost due to friction, PE1 must be equal to K2. Given that, can you figure the rest out? (Hint: set up the equation PE1=K2)
 
v = sqrt (2gy)
v = sqrt (2 * 9.8m/ss * 35m) = 26.19 m/s at point 2

But K2 doesn't equal P2 because K2 equaled P1 at a height of 35m, not 28m, right?
 
But K2 doesn't equal P2 because K2 equaled P1 at a height of 35m, not 28m, right?

I don't know if I understand this question. Did you mean to say "But K2 doesn't equal P3 because K2..."? If you were asking about how to solve for velocity at P3, do you think you could use a similar strategy that you did for point P2? It may help if I point out that you are indirectly given the difference in height between P1 and P3.
 

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